In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This article for primary teachers suggests ways in which to help children become better at working systematically.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many different triangles can you make on a circular pegboard that has nine pegs?
How many trains can you make which are the same length as Matt's, using rods that are identical?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Find out about Magic Squares in this article written for students. Why are they magic?!
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Can you find all the different ways of lining up these Cuisenaire
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
Can you fill in the empty boxes in the grid with the right shape
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Find out what a "fault-free" rectangle is and try to make some of
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
An investigation that gives you the opportunity to make and justify
Number problems at primary level that require careful consideration.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Can you find the chosen number from the grid using the clues?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?